What makes car to accelerate?

The force acting on a car in vertical direction cancel out(the gravitational force and the normal force) such that it doesn't move in vertical direction.

If the car were to move to the right on a road, we are supposed to provide a force to the car by imagining that we can use our hands to push the car from the back.

However, I find it odd to think of how can the engine provide the force to the car since the engine is in the system. The force provided by pushing using hands from the back are from external agent.

It's confusing to think of how can the internal system-the engine supplies force to itself and make itself moves. Just like an astronaut floating in the space is unable to move unless someone else push/pull him.

The force acting on a car in vertical direction cancel out(the gravitational force and the normal force) such that it doesn't move in vertical direction.

If the car were to move to the right on a road, we are supposed to provide a force to the car by imagining that we can use our hands to push the car from the back.

However, I find it odd to think of how can the engine provide the force to the car since the engine is in the system. The force provided by pushing using hands from the back are from external agent.

It's confusing to think of how can the internal system-the engine supplies force to itself and make itself moves. Just like an astronaut floating in the space is unable to move unless someone else push/pull him.

Thank you.

The engine applies force to the wheels which push back on the road. The car, after all, is connected to the earth unlike an astronaut.

The wheels of the car pushes on the road like Andrew said. The road pushes back on the wheels via Newton's third law. This force coming from the road pushes the car forward (weird as it seems, but if the surface consists of loose gravel the car cannot get traction - the wheels just spin around. Which tells us the force coming from the surface is actually responsible for the forward motion of the car.).

Thanks for your answers. I can finally imagine how it actually occurs.

Putting the walking of a person as an example.
The person tries to walk by pulling the earth and at the same time Newton's third law says the earth will push you foward with the same force as well, thus enabling you to walk.